# Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases

arXiv: https://arxiv.org/abs/1608.04219 · HTML: https://mlsanity.com/paper/1608.04219/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2016.

## Built on by (most cited first, 4 of 4)

- [Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/2304.12154/) (2023)
- [Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD](https://mlsanity.com/paper/2401.13343/) (2024)
- [Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems](https://mlsanity.com/paper/2404.17508/) (2024)
- [Learning Fast Monomial Orders for Gr"obner Basis Computations](https://mlsanity.com/paper/2602.02972/) (2026)

## Abstract (arXiv)

Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polynomials using Groebner Basis (GB) theory. Previous experiments have shown that while this can often be very beneficial to the CAD algorithm, for some problems it can significantly worsen the CAD performance. In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning. We run experiments with over 1000 problems (many times larger than previous studies) and find that the machine learned choice does better than the human-made heuristic.